1.1.

Phenomenology

Soil particles consist mostly of rock-forming minerals. In the presence of external forces and charges, the ionic bonds that make up these minerals will stretch and vibrate. Fundamental molecular vibrations are known as reststrahlen, and the acoustical features that are present in the spectral emissivity signatures of quartz-based soil are called reststrahlen bands. These bands correspond to a sudden decrease in emissivity. Two notable reststrahlen band emissivity troughs can be sensed between 7.5 and $10\mu \mathrm{m}$.

It is the magnitude of the reststrahlen emissivity troughs that can be used as target identifiers. Even when quartz is a minority component within a mixture, quartz reststrahlen bands tend to dominate the shape of the corresponding spectral curves.⁶ The addition of other minerals has a broadening effect upon the emissivity troughs. It should also be noted that both the magnitude and shape of the reststrahlen bands are impacted by the variety and color of quartz that is measured.

Spectral contrast is another identifiable feature observed in the hyperspectral description of soils. With respect to quartz-based sand, this contrast refers to the height of the emissivity peak that separates the two notable emissivity troughs in the $7.5–10\mu \mathrm{m}$ region of the long-wave infrared (LWIR) spectrum. In 1964, Lyon observed that the spectral contrast in this wavelength regime was dependent upon particle size.⁷ Further, contrast tends to decrease with decreasing particle size. Salisbury and Wald proposed that the dominating volume scatter of optically thin grains is the primary impetus for reduced spectral contrast within the reststrahlen region.⁸ He also explained the indirect link between contrast and the porosity of granular soil targets. Soils with high levels of porosity allow for the incoherent scattering of individual quartz particles, and exhibit higher emissivity and less contrast than do closely packed sand samples. Additional observations by Johnson et al.¹ affirmed the relationship between soil emissivity and porosity. Bachmann et al. highlighted the difficulties surrounding the inclusion of porosity and particle size effects within physical reflectance models.⁹ It has been shown here that geometry certainly impacts the ability to discern between soil targets. Prior to this work, the geometric aspects of particle shape, size, and spacing have not been adequately integrated into a model to predict complex soil signatures.

Soil emission phenomenology cannot be thoroughly discussed without acknowledging the influence of material chemistry. In the $7.5–10\mu \mathrm{m}$ regime, optical properties of quartz vary. Moersch and Christensen explain that due to the high imaginary component of the complex index of refraction, specular Fresnel reflections dominate the spectral region defined by the reststrahlen emissivity troughs.¹⁰ Because of these reflections, thermal energy cannot easily propagate through soil grains in a medium. Stifled radiation transport in this spectral region leads to the formation of emission troughs. This effect poses an interesting modeling problem. The optical properties of large quartz particles and tiny quartz particles are the same. Yet, small quartz particles display much higher emissivity than larger grains of the very same material. Moersch and Christensen explain that the likelihood of emission from particles depends on the coupled relationship between particulate geometry and chemistry. Radiation within a small particle will interact with the grain boundary more frequently before reabsorption than will radiation in a larger particle (Fig. 1).

Fig. 1

Prereabsorption interactions between thermal radiation and grain boundaries depend on particle size. When compared to small particles, radiation emitted from large grains travels a longer optical path to experience the same number of radiation-boundary interactions.

Therefore, radiation within smaller particles has a greater chance of being emitted and propagated to a sensor at certain wavelengths. In this specific trade-space of geometry and chemistry, geometry seems to impact the detectability of the signature most. We do not presume to say that the optical properties of quartz in this region do not contribute to the presence of emission troughs. We only contend that the spectral identifiers of emissivity magnitude and spectral contrast are spawned from a dependent relationship.

1.2.

Modeling Phenomenology

This discussion has named several of the subprocesses that are associated with radiation scatter and emission. A true description of scatter should include each and every physical trait that contributes to reflection and emission. Omission of phenomenology leads to false attribution of physical effects within a model. The result is a tool that may be force fitted to describe a target with accuracy. Such an algorithm may not be invertible. It would produce an unphysical result for other samples that scatter light differently. Surely, the failure to include necessary scattering parameters makes simulation difficult. Presuming all physical scatter contributions could be included, modeling them all in parallel is a daunting task. This would likely require many different properties to be specified and not every parameter can be independently modeled. This is why appending physical considerations to existing models should be done with care.^11,12 Important relationships between geometric, radiometric, and chemical parameters must be acknowledged. If certain parameters are underestimated or incompletely described in an algorithm, there exists a need for unphysical scaling factors.¹¹

1.3.

Modeling with Digital Imaging and Remote Sensing Image Generation and Blender Three-Dimension

It is important to state what this model is not. The method described in this paper is not an attempt to explicitly solve for all physical and chemical phenomenology associated with the reflection and emission of complex soils. It is not a parameter-based model containing arbitrary functions that are fit to data curves. This procedure will not approximate surface geometry as a probabilistic distribution of facets.¹² It does not presume that a surface of thousands of irregular particles will scatter as a linear combination of individual phase functions solved independently of one another.¹¹

This is a method focused on scene geometry that simulates the reflectance and emissivity of complex mixtures of solids. This is an avenue to explore the phenomenology of particle size distribution, density, and intimate mixing. Most importantly, the model bundles together the chemical, radiometric, and geometric components of material signatures.

Chemical parameters to be considered in a soil scattering model include indices of refraction, absorption, anomalous dispersion, anisotropy, and lattice vibrations. Solving for each of these constraints is very difficult. Instead, measured emissivity spectra of pure materials are used in this simulation procedure. For instance, soil particles in this model that possess a $50\mu \mathrm{m}$ radius are attributed with the emissivity spectra of $50\mu \mathrm{m}$ soil.

The radiometric aspects of this simulation are solved using the DIRSIG model. DIRSIG is a first principle-based ray-tracing model that produces at-sensor radiance.^13,14 Light sources, scene geometries, and sensor configurations are all defined by the user (Fig. 2). This model has been predominantly used for the analysis and modeling of sensors. DIRSIG allows for direct system comparisons. A single scene can be observed under varying atmospheric conditions, with multimodal sensing techniques. Though it is easy to conceptualize passive remote sensing as light rays traveling from source to target to sensor, DIRSIG models radiation in inverse fashion, using backward ray tracing. Rays are initially cast from individual pixels of a user-defined focal plane array. These rays determine what each pixel sees and where radiation originates.

Fig. 2

The versatility of digital imaging and remote sensing image generation (DIRSIG) lies in user control. Within a single simulation, each link of the imaging chain can be modeled with precision. The input of the chain is a uniquely defined scene and irradiance level. The output is a radiance image produced by a virtual sensor. Links of the chain include the light source, radiation propagation, target geometry, atmosphere, and the sensor. Parameters of each link are defined prior to simulation. Since the model is compartmentalized, scenarios can be changed with precision and with ease.

The geometry of soil is created using the Blender three-dimensional (3-D) open source graphic design software. This design suite gives users the ability to etch, bend, and connect different shapes or planes to create objects with precision. Using built-in physics engines, one can create a scene of objects that interact based on the physical properties (mass and shape) defined by the user. Simulating rigid body collisions, fluid motion, and force field interactions is all possible using the Blender 3-D tool. Each mesh object is subjected to friction and damping, and interacts with other objects through collisions based on mass. Individual mesh facets influence collisions between in-scene objects. This implies that a convex hull does not define the physical bounds of a soil particle created in Blender 3-D. For instance, a multifaceted particle is bounded by its facets rather than a sphere or a six-sided cube with similar volume.

2.1.

Geometry

This model of disturbed soil begins with a geometric description at the microscopic scale. As alluded to the introduction, mesh objects of different geometries are rotated, translated, and extruded to produce objects that match the 3-D geometry of soil grains. Scanning electron microscope (SEM) images provided a visual template for particle design. An example image can be seen in Fig. 3.

Fig. 3

(a) A soil particle covered in dust grains is one example of precise geometric modeling that is native to Blender three-dimension. (b) Scanning electron microscope images reveal small dust particles clinging to larger grains.¹

In previous discussion, it was explained that weathering and human disturbance contribute to the distribution of different particle sizes within a target sample. It was observed that small fine particles cling to larger soil particles when the ground soil is sifted or dug up and overturned.^1,8 The presence of the fine dusting, combined with altered porosity, distinctly changes the magnitude and shape of sample spectral signatures. The scene built to model disturbed soil included superfine dust grains clinging to larger sand or soil particles. Two separate shapes with average diameters of 60 μm and 35 μm were used to represent fine dust particles. Three other shapes represented large grains. These three particles had average diameters of $500\mu \mathrm{m}$, $640\mu \mathrm{m}$, and $853\mu \mathrm{m}$, respectively. Each of the five shapes was created manually using SEM imagery as a template. In Blender 3-D, a dusty sand particle was created through a simple process. First, a large grain particle (500 to $853\mu \mathrm{m}$) was designed. Then a multitude of superfine particles was formed. Next, the facets of the large grains were subdivided into smaller facets that have a diameter that is close in size to the dusty fines. By manually aligning particle faces, each piece of dust was easily abutted to the larger particle. A parent–child relationship was set between the large grain and the fine particulates. This ensured that the large grain and the dust grains remained in contact during rigid body simulation. This also allowed for grains of each size to be assigned their own unique material spectra before the final geometry was exported to DIRSIG. A Blender 3-D representation of a dusty particle is depicted in Fig. 3.

Realistic scene posing and mixing were performed using the Blender 3-D physics engine. To model a natural soil scene, particles were not individually placed by hand. User placement of thousands of objects would be incredibly tedious and likely unphysical. Each particle was treated as a rigid body and was dropped onto a surface where particle interactions occurred. Grains eventually settled into a physical 3-D soil scene. This process is illustrated in Fig. 4.

Fig. 4

The process of scene building is based upon physics engines in Blender 3-D. Above, particles fall onto a surface where they settle naturally in space. A video of this process can be viewed online.¹⁵

In the graphic design software, this soil scene simulation takes the form of a motion picture. At each frame, particle position was calculated using the mass, shape, and external forces of gravity and inter-particle collisions. A single frame was used as the target description within the DIRSIG radiometry solver. This geometry included the position in $x,y,z$ coordinates of all object vertices. It is an actual record of particle shape and position that forms an accurate account of particle distribution and spacing.

2.2.

Chemistry

Before the soil grains were inserted into a DIRSIG radiometry simulation, emissivity spectra were assigned to the facets of each particle. Spectral reflectance and emissivity response curves represent how each facet will respond to interaction with a photon. It is known that large and small quartz particles have distinct LWIR spectra due to the incoherent emission of radiation.⁸ The directional hemispherical reflectance spectra of quartz have been published for many specific size distributions (including $50\mu \mathrm{m}$ grains).^1,16 These data were extracted and converted into DIRSIG emissivity files.

2.3.

Radiometry

Radiance that is measured by a DIRSIG imager or a laboratory sensor has multiple components. Radiation leaves a target to be detected through the processes of reflection ($L_r$) and emission ($L_e$). Radiance upwelling ($L_u$) from the ground/target plane is a linear combination of these two processes

To know target emissivity, the emissive and reflective components of Eq. (1) must be separated. Empirical methods used to separate these terms are nontrivial. To calculate emissivity, downwelling radiance ($L_d$) must be known or measured. Downwelling radiance is the radiation from the sky or a light source that illuminates a target. The equation used in DIRSIG and in the laboratory to find spectral emissivity is

Obtaining emissivity using Eq. (2) is a conditional process.¹⁷ When the temperature of the downwelling atmosphere is similar to that of the target, there is little contrast between values in the numerator of Eq. (2). This results in small emissivity values that may be dominated by noise. Also, if the values in the denominator of Eq. (2) have similar magnitudes, the emissivity equation becomes unstable. For these reasons, performing good emissivity measurements in the field or laboratory is hard to do. On very clear days, downwelling radiance ($L_d$) is relatively stable and the sky is usually much colder than the sample of interest. In this scenario, Eq. (2) provides good results. When conditions are imperfect, the sample temperature and the atmospheric temperature are knowingly altered in experimental situations in order to increase the contrast between radiance values. The accuracy of the emissivity results also depends on how well the temperature of the sample is known. Temperature emissivity separation and curve smoothing techniques are often employed to find actual temperatures from a selection of probable temperatures.¹⁸

Using DIRSIG to simulate emissivity data does require some experimental manipulation, but the process is relatively easy and does not call for the postprocessing described above. Users have control of in-scene radiance sources. By removing these sources, the downwelling radiance ($L_d$) term in Eq. (2) is nullified and a simple ratio remains

DIRSIG allows in-scene objects to be attributed with a specific temperature. This implies that the user can define the temperature of an object, and blackbody radiance ($L_{\mathrm{BB}}$) is completely known. The user’s control of radiation sources and temperature allows for emissivity to be solved painlessly.

With this theory in mind, the process to create emissivity simulations can be defined. First, import geometry into DIRSIG using. obj files. These files contain the locations of all the vertices and edges of objects in the target scene. Next, multiple instances of target geometry are defined within a. odb file. This allows for the size of a target to be expanded. Material (.mat) files are configured to link temperature and wavelength-dependent spectral properties to facets in the scene. In this study, a temperature of 300 K was used to define target radiance and blackbody radiance. To impose the conditions of Eq. (3), irradiance from the in-scene light source is set to zero. This parameter is set within the atmosphere (.atm) file. Last, sensor geometry and response are defined. The sensor used in simulation must be configured within the platform file to be responsive in the desired wavelength range. A spectral resolution of 10 nm was used in this work.

Using the scenes and modeling techniques described above, the LWIR soil signatures in the reststrahlen bands can be modeled. Emissivity can be found for a sample of disturbed soil. DIRSIG provides user control of temperature and source radiance, which allows for reflection and emission to be evaluated separately. This process provides a method to simulate in situ soil signatures. Recreation of such scenes is difficult in a laboratory setting.¹